Structural Engineering & Statics
where the load goes
Generator

The self-excitation generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
The damping a crowd leaves behind, and the number of people that uses it upTotal damping ratio against pedestrians, for a structure with 0.60% of its own and a modal mass of 120 tonnes at 0.5 Hz. Each person walking laterally puts a force in phase with the deck's velocity into it — about 300 N·s/m per person — so the crowd subtracts from the damping, and at 30.16 people what is left is nothing. Below the threshold a disturbance dies away. Above it, the structure feeds itself and the motion grows out of nothing at all — which is what makes this a different mechanism from resonance rather than a severe case of it.020406080100120-0.015-0.01-0.0050.005people walking on the spantotal damping ratio0.60% damping · 0.5 Hz30.16 people — nothing leftbelow: a disturbance dies awayabove: the structure drives itself

2 essays call self-excitation. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

020406080100120-0.015-0.01-0.0050.005people walking on the spantotal damping ratio0.60% damping · 0.5 Hz30.16 people — nothing leftbelow: a disturbance dies awayabove: the structure drives itself Dynamics

The bridge that was pushed by its own sway

A crowd walking on a bridge that moves sideways adjusts its footing to stay balanced, and the adjustment pushes the bridge the way it is already going. The crowd is a damper with the sign reversed, and past a certain number of people the total damping is negative.

 024681012-0.01-0.0050.005wind speed (m/s)total damping ratio0.60% damping · 1.2 Hz4.14 m/s — nothing leftbelow: a disturbance dies awayabove: the structure drives itself Dynamics

The motion that feeds itself

A steady wind contains no frequency at all, and it can destroy a bridge. The force that does it is manufactured by the structure's own movement, so there is no excitation to resonate with — there is a wind speed above which the equilibrium is unstable, and below which nothing happens.

The library, page 3 of 4 — where self-excitation sits